Second order differential (SOD) microphones have long been recognized for their superior noise cancelling performance relative to first order differential (FOD) or zero order differential (pressure) microphones. Early workers conceived making a SOD microphone by combining the outputs of two FOD microphones, or by combining the outputs of three or four pressure microphones. Such an approach requires the use of microphones whose amplitude and phase responses are very well matched.
Before electret microphones became available, typical off-the-shelf microphones did not exhibit the required match in amplitude and phase responses. Consequently, to produce a working SOD microphone with the then-existing technology, it was necessary to use a single FOD microphone with four distinct parts arranged to communicate equivalently with the microphone diaphragm. Single diaphragm SOD microphones were designed and built using, for example, either a moving coil or piezoelectric transducer mounted within an enclosure having sound ports to spatially sample the sound field. (See, for example, A. J. Brouns, "Second-Order Gradient Noise-Cancelling Microphone," IEEE International Conference on Acoustics, Speech, and Signal Processing CH1610-5/81 (May 1981) 786-789, and W. A. Beaverson and A. M. Wiggins, "A Second-Order Gradient Noise Canceling Microphone Using a Single Diaphragm," J. Acoust. Soc. Am. 22 (1950) 592-601.)
In some implementations, for example, the ports were placed symmetrically, at the four corners of a square, around the FOD microphone to ensure that the acoustic response of the diaphragm to each of the ports was identical. These single diaphragm SOD microphones produced an output signal proportional to the biaxial second order derivative ##EQU1## of the sound pressure field.
A later implementation, described in G. M. Sessler, and J. E. West, "Second order gradient uni-directional microphones utilizing an electret transducer," J. Acoust. Soc. Amer. 58 (1975) 273-278, incorporated an electret microphone element in a single diaphragm SOD microphone. Specifically, an experimental unidirectional SOD microphone was fabricated using an electret microphone into which tubes were inserted to sample the sound field at discrete points along an axis. (By "unidirectional" is meant that the microphone far-field sensitivity pattern is distinctly peaked in a preferred direction.) The tube lengths and their positions in the front and rear cavities of the electret microphone were chosen to produce the desired unidirectional far-field response.
In order to achieve the desired second-order behavior, it was necessary to precisely tune the Helmholtz resonances of the cavities and the sensing tubes. The effort involved in this tuning operation detracted from the practicality of mass producing this SOD microphone.
We have found that when a SOD microphone is configured to produce an output signal proportional to the uniaxial second order derivative ##EQU2## instead of the biaxial derivative of the sound pressure field, it can take better advantage of the spherical wave nature of a speaker's voice field to maximize sensitivity to the speaker's voice. This property is discussed, for example, in a co-pending United States patent application filed by C. Bartlett and M. Zuniga on Apr. 21, 1994 under the title, "Noise-Canceling Differential Microphone Assembly."
Practitioners in the field of microphone design have hitherto failed to provide a single diaphragm SOD microphone that is easy to mass produce, and that has an output proportional to a uniaxial second order derivative ##EQU3## of the acoustic pressure field.